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Computerized classification tests (CCT) have been used in high-stakes assessment settings where the express purpose of the testing is to assign a classification decision (e.g. pass/fail). One key feature of sequential probability ratio test-type procedures is that items are selected to maximize information around the cutscore region of the examinee ability distribution as opposed to common features of CATs where items are selected to maximize information at examinees' interim estimates. Previous research has examined the effectiveness of computerized adaptive tests (CAT) utilizing classification testing procedures a single cutscore as well as multiple cutscores (e.g. below basic/proficient/advanced). Several variations of the SPRT procedure have been advanced recently including a generalized likelihood ratio (GLR). While the GLR procedure has shown evidences of improved average test length while reasonably maintaining classification accuracy, it also introduces unnecessary error. The purpose of this dissertation was to propose and investigate the functionality of a modified GLR procedure which does not incorporate the unnecessary error inherent in the GLR procedure. Additionally this dissertation explored the use of the multiple cutscores and the use of ability-based item selection. This dissertation investigated the performance of three classification procedures (SPRT, GLR, and modified GLR), multiple cutscores, and two test lengths. An additional set of conditions were developed in which an ability-based item selection method was used with the modified GLR. A simulation study was performed to gather evidences of the effectiveness and efficiency of a modified GLR procedure by comparing it to the SPRT and GLR procedures. The study found that the GLR and mGLR procedures were able to yield shorter test lengths as anticipated. Additionally, the mGLR procedure using ability-based item selection produced even shorter test lengths than the cutscore-based mGLR method. Overall, the classification accuracy of the procedures were reasonably close. Examination of conditional classification accuracy in the multiple-cutscore conditions showed unexpectedly low values for each of the procedures. Implications and future research are discussed herein. / text

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Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection.

Online process monitoring and feedback control are two widely researched aspects that can impact the performance of a myriad of process applications. Semiconductor manufacturing is one such application that due to the ever increasing demands placed on its quality and speed holds tremendous potentials for further research and development in the areas of monitoring and control. One of the key areas of semiconductor manufacturing that has received significant attention among researchers and practitioners in recent years is the online sensor based monitoring and feedback control of its nanoscale wafer fabrication process. Monitoring and feedback control strategies of nanomanufacturing processes often require a combination of monitoring using nonstationary and multiscale signals, and a robust feedback control using complex process models. It is also essential for the monitoring and feedback control strategies to possess stringent properties such as high speed of execution, low cost of operation, ease of implementation, high accuracy, and capability for online implementation. Due to the above requirement, a need is being felt to develop state-of-the-art sensor data processing algorithms that can perform far superior to those that are currently available both in the literature and commercially in the form of softwares.The contributions of this dissertation are three fold. It first focuses on the development of an efficient online scheme for process monitoring. The scheme combines the potentials of wavelet based multiresolution analysis and sequential probability ratio test to develop a very sensitive strategy to detect changes in nonstationary signals. Secondly, the dissertation presents a novel online feedback control scheme. The control problem is cast in the framework of probabilistic dynamic decision making, and the control scheme is built on the mathematical foundations of wavelet based multiresolution analysis, dynamic programming, and machine learning. Analysis of convergence of the control scheme is also presented. Finally, the monitoring and the control schemes are tested on a nanoscale manufacturing process (chemical mechanical planarization, CMP) used in silicon wafer fabrication. The results obtained from experimental data clearly indicate that the approaches developed outperform the existing approaches. The novelty of the research in this dissertation stems from the fact that they further the science of sensor based process monitoring and control by uniting sophisticated concepts from signal processing, statistics, stochastic processes, and artificial intelligence, and yet remain versatile to many real world process applications.

This dissertation mainly consists of three parts. The first part proposes generalized linear minimum mean-square error (GLMMSE) estimation for nonlinear point estimation. The second part proposes a recursive joint decision and estimation (RJDE) algorithm for joint decision and estimation (JDE). The third part analyzes the performance of sequential probability ratio test (SPRT) when the log-likelihood ratios (LLR) are independent but not identically distributed. The linear minimum mean-square error (LMMSE) estimation plays an important role in nonlinear estimation. It searches for the best estimator in the set of all estimators that are linear in the measurement. A GLMMSE estimation framework is proposed in this disser- tation. It employs a vector-valued measurement transform function (MTF) and finds the best estimator among all estimators that are linear in MTF. Several design guidelines for the MTF based on a numerical example were provided. A RJDE algorithm based on a generalized Bayes risk is proposed in this dissertation for dynamic JDE problems. It is computationally efficient for dynamic problems where data are made available sequentially. Further, since existing performance measures for estimation or decision are effective to evaluate JDE algorithms, a joint performance measure is proposed for JDE algorithms for dynamic problems. The RJDE algorithm is demonstrated by applications to joint tracking and classification as well as joint tracking and detection in target tracking. The characteristics and performance of SPRT are characterized by two important functions—operating characteristic (OC) and average sample number (ASN). These two functions have been studied extensively under the assumption of independent and identically distributed (i.i.d.) LLR, which is too stringent for many applications. This dissertation relaxes the requirement of identical distribution. Two inductive equations governing the OC and ASN are developed. Unfortunately, they have non-unique solutions in the general case. They do have unique solutions in two special cases: (a) the LLR sequence converges in distributions and (b) the LLR sequence has periodic distributions. Further, the analysis can be readily extended to evaluate the performance of the truncated SPRT and the cumulative sum test.

The tremendous success of various wireless applications operating in unlicensed bands has resulted in the overcrowding of those bands. Cognitive radio (CR) is a new technology that enables an unlicensed user to coexist with incumbent users in licensed spectrum bands without inducing interference to incumbent communications. This technology can significantly alleviate the spectrum shortage problem and improve the efficiency of spectrum utilization. Networks consisting of CR nodes (i.e., CR networks)---often called dynamic spectrum access networks or NeXt Generation (XG) communication networks---are envisioned to provide high bandwidth to mobile users via heterogeneous wireless architectures and dynamic spectrum access techniques. In recent years, the operational aspects of CR networks have attracted great research interest. However, research on the security aspects of CR networks has been very limited. In this thesis, we discuss security issues that pose a serious threat to CR networks. Specifically, we focus on three potential attacks that can be launched at the physical or MAC layer of a CR network: primary user emulation (PUE) attack, spectrum sensing data falsification (SSDF) attack, and control channel jamming (CCJ) attack. These attacks can wreak havoc to the normal operation of CR networks. After identifying and analyzing the attacks, we discuss countermeasures. For PUE attacks, we propose a transmitter verification scheme for attack detection. The scheme utilizes the location information of transmitters together with their signal characteristics to verify licensed users and detect PUE attackers. For both SSDF attacks and CCJ attacks, we seek countermeasures for attack mitigation. In particular, we propose Weighted Sequential Probability Ratio Test (WSPRT) as a data fusion technique that is robust against SSDF attacks, and introduce a multiple-rendezvous cognitive MAC (MRCMAC) protocol that is robust against CCJ attacks. Using security analysis and extensive numerical results, we show that the proposed schemes can effectively counter the aforementioned attacks in CR networks. / Ph. D.

This paper deals with sequential likelihood ratio tests based on grouped observations. It is demonstrated that the method of conjugated parameter pairs known from the non-grouped case can be extended to the grouped case obtaining Waldlike approximations for the OC- and ASN- function. For near hypotheses so-called F-optimal groupings are recommended. As example an SPRT based on grouped observations for the parameter of an exponentially distributed random variable is considered.

This paper deals with the computation of OC- and ASN-function of sequential probability ratio tests in the multi-parameter case. In generalization of the method of conjugated parameter pairs Wald-like approximations are presented for the OC- and ASN-function. These characteristics can be used describing robustness properties of a sequential test in case of nuisance parameters. As examples tests are considered for the mean and the variance of a normal distribution.